Conventional systems and methods utilize a static pump reference model for a fracking rig pump. The reference model may be used, for example, for diagnostics of the fracking rig pump. The reference model requires a choke area (or, a restriction area) associated with the fracking rig pump to calculate a pressure signal. For example, the choke area may be present at a well-head of a fracking rig site, or along any path of the flow of fluid through the fracking rig pump. Further, multiple fracking rig pumps are generally present in the fracking rig site, all feeding to the well-head. However, the choke area changes due to different customer requirements or different stages of drilling procedure with different pump speeds on a fracking rig worksite. In practice, a change in the choke area can be realized by physical valve opening or closing. In conventional pump models that do not have valve dynamics included, there is no way to compensate for the change in the choke area in the fracking rig pump model itself. However, including valve dynamics in the reference model is often too complicated and may be unnecessary for the control purposes for which the reference model is used.
One conventional solution is to use a three-dimensional (3D) map to find an approximate value of the choke area. Given a set of maximum power, maximum pressure, and a pump speed, the choke area is approximated based on the 3D map. The 3D map is pre-calculated and is static. That is, any other set of values that is not on the nodes of the 3D map will be calculated using an interpolation method. Furthermore, the 3D map has shortcomings. For example, generating the 3D map is very time consuming, requiring manual tuning. The interpolation method is linear and not very accurate, since a relationship between the choke area and the pump parameters are not exactly known. In order to make the 3D map more accurate, a higher number of nodes in the 3D map is needed, and more nodes means more manual tuning of the map. Moreover, the 3D map is valid for one pump. If any parameter of the rig pump changes, all the tuning work of the 3D map needs to be redone. By way of example only, U.S. patent Application Publication No. 2014/0094974 discloses a conventional method in which an interpolation model for interpolating data over a domain defined by operational bounds of two control variables of a fluid production method is described.
The present disclosure addresses these problems and other problems associated with the conventional systems and methods.